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wu :: forums    riddles    general problem-solving / chatting / whatever (Moderators: towr, Icarus, ThudnBlunder, william wu, Eigenray, SMQ, Grimbal)    apparent area/position function « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: apparent area/position function  (Read 500 times) jarls Newbie     Posts: 32 apparent area/position function   « on: Jan 13th, 2009, 2:39pm » Quote Modify An observers stands with eyes at a fixed location. An object moves away from the observer linearly with constant velocity and along the observer's line of sight/parallel to the observer's line of sight but not along it. What function designates the rate of change in the object's apparent area (imagine holding up tracing paper in front of the eyes and tracing the object) of the object for the observer with respect to time where velocity is some constant? If the trajectory of the object does not lie along the observer's line of sight what function designates at what rate it will appear to approach the line of sight of the observer? « Last Edit: Jan 13th, 2009, 2:43pm by jarls » IP Logged Grimbal wu::riddles Moderator Uberpuzzler     Gender: Posts: 7527 Re: apparent area/position function   « Reply #1 on: Jan 14th, 2009, 5:22am » Quote Modify The size of the object would be proportional to 1/t where t is the time from the moment the object was closest to the observer.  I assume a projection on a plane perpendicular to the line of sight. The area would be ~1/t2. « Last Edit: Jan 14th, 2009, 5:23am by Grimbal » IP Logged jarls Newbie     Posts: 32 Re: apparent area/position function   « Reply #2 on: Jan 14th, 2009, 7:44pm » Quote Modify What would the function be? IP Logged teekyman Full Member     Gender: Posts: 199 Re: apparent area/position function   « Reply #3 on: Jan 14th, 2009, 11:15pm » Quote Modify since the object is off to the side of you, if it gets really close the apparent area will go to 0 again. I don't know if there's a way to avoid some messyish trig. IP Logged Grimbal wu::riddles Moderator Uberpuzzler     Gender: Posts: 7527 Re: apparent area/position function   « Reply #4 on: Jan 15th, 2009, 5:18am » Quote Modify The position on the screen will be something like   (x,y) = (x0,y0)·(1/(t-t0)).   t0 is the time the object passes by the observer (x0,y0) is the position on the screen at t=1. IP Logged Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy   - medium   - hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ => general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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